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On the Consistency Rule in Causal Inference: An Axiom, Definition, Assumption, or a Theorem?


Remove the abstract (and move to the Main Text). In two recent communications, Cole and Frangakis and VanderWeele conclude that the consistency rule used in causal inference is an assumption that precludes any side-effects of treatment/exposure on the outcomes of interest. They further develop auxiliary notation to make this assumption formal and explicit. I argue that the consistency rule is a theorem in the logic of counterfactuals and need not be altered, even in cases where different versions of treatment/exposure have side effects on the outcome. Instead, warnings of potential side-effects should be embodied in standard modeling practices, using graphs or structural equation models, in which causal assumptions are given transparent and unambiguous representation.

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